Examples of recombinases known to be used in the conventional technology include HO endonuclease (e.g., see the specification of U.S. Pat. No. 6,037,162), I-SceI (for example, see the specification of U.S. Pat. No. 6,610,545; Jacquier et al., 1985. Cell, 41: 383-394; and Rouet et al., 1994. Proc. Natl. Acad. Sci. U.S.A., 91: 6064-6068), and Cre-lox (for example, see DiSanto et al., 1995. Proc. Natl. Acad. Sci. U.S.A. 92: 377-381). These enzymes are of a type of site-specific recombinase that exerts the functions via its introduction into cells. These enzymes extremely strictly recognize sequences and have no cleavage sites in heterologous genomes. These cleavage sequences are previously introduced into genomes, so that only the homologous recombination in the peripheries thereof can be activated. However, unlike the present invention, these enzymes cannot be used in principle for improving recombination frequency in general genomes. Regarding techniques for increasing recombination frequency at general positions in genomes using DNA-cleaving enzymes, no useful systems have been established. This is because the activity of a cleavage enzyme cannot be strictly controlled, thus likely causing a lethal effect on the cells. A similar conventional technique, an REMI method (Restriction Enzyme-Mediated Integration) (e.g., the specification of U.S. Pat. No. 5,792,633; Schiestl and Petes, 1991. Proc. Natl. Acad. Sci. U.S.A. 88: 7585-7589; and Schiestl et al., 1994. Mol. Cell. Biol. 14: 4493-4500) involves, upon transformation, mixing a restriction enzyme with DNA and then introducing the mixture into cells, so as to make it possible to increase the frequency of inserting the introduced DNA into the chromosome. However, with such a technique, DNA and a restriction enzyme can be incorporated into only small number of cells and the enzyme activity cannot be controlled. Hence, the use of such a technique is limited to only the promotion of the insertion of a foreign DNA into a chromosome. These conventional techniques have an essential drawback such that they cannot be used for large-scale genome composition alteration, such as genome shuffling.